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If 4x(5n) = t and x and n are integers, what is the value of t ? [#permalink]

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21 Dec 2016, 05:43

Official Explanation:

Quote:

4x(5n) is equivalent to 20xn, so to find the value of t, you need the value of xn. Statement (1) is sufficient: there is only one perfect square that is less than 250 and divisible by 20: 100. (t must be divisible by 20 because x and n must be integers.) Statement (2) is also sufficient: it directly gives us the information we need: the value of xn. Choice (D) is correct.

For (1): While i understand that 100 is the only perfect square less than 250 and divisible by 20, i would like to ask you guys what´s wrong with the following approach:

Given from (1): 20xy < 250 -> xy < 12.5

So there are basically two perfect squares below 12.5 -> 4 and 9. So x and y (both integers) are either 2 and 2 or 3 and 3, hence the statement should be insufficient.

Can anyone (...or @Bunuel) explain the mistake in my thought process?

If 4x(5n) = t and x and n are integers, what is the value of t ? [#permalink]

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21 Dec 2016, 06:38

1

This post was BOOKMARKED

paddy41 wrote:

Official Explanation:

Quote:

4x(5n) is equivalent to 20xn, so to find the value of t, you need the value of xn. Statement (1) is sufficient: there is only one perfect square that is less than 250 and divisible by 20: 100. (t must be divisible by 20 because x and n must be integers.) Statement (2) is also sufficient: it directly gives us the information we need: the value of xn. Choice (D) is correct.

For (1): While i understand that 100 is the only perfect square less than 250 and divisible by 20, i would like to ask you guys what´s wrong with the following approach:

Given from (1): 20xy < 250 -> xy < 12.5

So there are basically two perfect squares below 12.5 -> 4 and 9. So x and y (both integers) are either 2 and 2 or 3 and 3, hence the statement should be insufficient.

Can anyone (...or @Bunuel) explain the mistake in my thought process?

Thank you!

I don't think that inequality is the right way to solve this question.

I'd better put it this way:

\(t^2 = 20xn\)

\(t = \sqrt{20xn} = 2*\sqrt{5xn}\)

For the expression under the radical to be an integer min value of \(xn\) can be \(5\). Either \(x=1\) and \(n=5\) or \(x=5\) and \(n=1\). In both cases we'll get our \(t\).

If you wish you can put it in the form of inequality:

\(2*\sqrt{5xn} < \sqrt{250}\)

or

\(2*\sqrt{5xn} < 5* \sqrt{10}\)

But I don't think this will help much, because you'll need to approximate \(5* \sqrt{10}\).

Re: If 4x(5n) = t and x and n are integers, what is the value of t ? [#permalink]

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21 Dec 2017, 10:27

Ans B.

St1: t=20xn is a perfect square below 250 and x&n are integers (can be positive, negative or zero) Therefore, there are two possible perfect squared values for t: 0 (x*n=0) and 100 (x*n=5) Insufficient

If 4x(5n) = t and x and n are integers, what is the value of t ? [#permalink]

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21 Dec 2017, 11:00

Shobhit7 wrote:

Ans B.

St1: t=20xn is a perfect square below 250 and x&n are integers (can be positive, negative or zero) Therefore, there are two possible perfect squared values for t: 0 (x*n=0) and 100 (x*n=5) Insufficient

St1: t=20xn is a perfect square below 250 and x&n are integers (can be positive, negative or zero) Therefore, there are two possible perfect squared values for t: 0 (x*n=0) and 100 (x*n=5) Insufficient